Number Theory

Por • 15 ago, 2021 • Sección: Ambiente

Number theory is a vast and fascinating field of mathematics, sometimes called «higher arithmetic,» consisting of the study of the properties of whole numbers. Primes and prime factorization are especially important in number theory, as are a number of functions such as the divisor functionRiemann zeta function, and totient function. Excellent introductions to number theory may be found in Ore (1988) and Beiler (1966). The classic history on the subject (now slightly dated) is that of Dickson (2005abc).

The great difficulty in proving relatively simple results in number theory prompted no less an authority than Gauss to remark that «it is just this which gives the higher arithmetic that magical charm which has made it the favorite science of the greatest mathematicians, not to mention its inexhaustible wealth, wherein it so greatly surpasses other parts of mathematics.» Gauss, often known as the «prince of mathematics,» called mathematics the «queen of the sciences» and considered number theory the «queen of mathematics» (Beiler 1966, Goldman 1997).

SEE ALSO:Abstract AlgebraAdditive Number TheoryAlgebraic Number TheoryAnalytic Number TheoryArithmeticComputational Number TheoryCongruenceDiophantine EquationDivisor FunctionElementary Number TheoryGödel’s First Incompleteness TheoremGödel’s Second Incompleteness TheoremMultiplicative Number TheoryNumber Theoretic FunctionPeano’s AxiomsPrime Counting FunctionPrime FactorizationPrime NumberQuadratic Reciprocity TheoremRiemann Zeta FunctionTotient Function


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Ayoub, R. G. An Introduction to the Analytic Theory of Numbers. Providence, RI: Amer. Math. Soc., 1963.

Beiler, A. H. Recreations in the Theory of Numbers: The Queen of Mathematics Entertains, 2nd ed. New York: Dover, 1966.

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Berndt, B. C. Ramanujan’s Notebooks, Part I. New York: Springer-Verlag, 1985.

Berndt, B. C. Ramanujan’s Notebooks, Part II. New York: Springer-Verlag, 1988.

Berndt, B. C. Ramanujan’s Notebooks, Part III. New York: Springer-Verlag, 1997a.

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Berndt, B. C. Ramanujan’s Notebooks, Part V. New York: Springer-Verlag, 1997b.

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Dickson, L. E. History of the Theory of Numbers, Vol. 1: Divisibility and Primality. New York: Dover, 2005a.

Dickson, L. E. History of the Theory of Numbers, Vol. 2: Diophantine Analysis. New York: Dover, 2005b.

Dickson, L. E. History of the Theory of Numbers, Vol. 3: Quadratic and Higher Forms. New York: Dover, 2005c.

Dudley, U. Elementary Number Theory. San Francisco, CA: W. H. Freeman, 1978.

Friedberg, R. An Adventurer’s Guide to Number Theory. New York: Dover, 1994.

Gauss, C. F. Disquisitiones Arithmeticae. New Haven, CT: Yale University Press, 1966.

Goldman, J. R. The Queen of Mathematics: An Historically Motivated Guide to Number Theory. Wellesley, MA: A K Peters, 1997.

Guy, R. K. Unsolved Problems in Number Theory, 3rd ed. New York: Springer-Verlag, 2004.

Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, 1979.

Hardy, G. H. Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, 3rd ed. New York: Chelsea, 1959.

Hasse, H. Number Theory. Berlin: Springer-Verlag, 1980.

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Ireland, K. F. and Rosen, M. I. A Classical Introduction to Modern Number Theory, 2nd ed. New York: Springer-Verlag, 1995.

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Lang, S. Algebraic Number Theory, 2nd ed. New York: Springer-Verlag, 1994.

Lenstra, H. W. and Tijdeman, R. (Eds.). Computational Methods in Number Theory, 2 vols. Amsterdam: Mathematisch Centrum, 1982.

LeVeque, W. J. Fundamentals of Number Theory. New York: Dover, 1996.

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Mitrinović, D. S. and Sándor, J. Handbook of Number Theory. Dordrecht, Netherlands: Kluwer, 1995.

Mollin, R. A. Algebraic Number Theory. Boca Raton, FL: CRC Press, 1999.

Mollin, R. A. Fundamental Number Theory with Applications. Boca Raton, FL: CRC Press, 1998.

Niven, I. M.; Zuckerman, H. S.; and Montgomery, H. L. An Introduction to the Theory of Numbers, 5th ed. New York: Wiley, 1991.

Ogilvy, C. S. and Anderson, J. T. Excursions in Number Theory. New York: Dover, 1988.

Ore, Ø. Invitation to Number Theory. Washington, DC: Math. Assoc. Amer., 1967.

Ore, Ø. Number Theory and Its History. New York: Dover, 1988.

Rose, H. E. A Course in Number Theory, 2nd ed. Oxford, England: Clarendon Press, 1995.

Rosen, K. H. Elementary Number Theory and Its Applications, 3rd ed. Reading, MA: Addison-Wesley, 1993.

Schroeder, M. R. Number Theory in Science and Communication: With Applications in Cryptography, Physics, Digital Information, Computing, and Self-Similarity, 3rd ed. New York: Springer-Verlag, 1997.

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Weyl, H. Algebraic Theory of Numbers. Princeton, NJ: Princeton University Press, 1998.

Yildirim, C. Y. and Stepanov, S. A. (Eds.). Number Theory and Its Applications. New York: Dekker, 1998.

Young, J. W. A. «The Theory of Numbers.» Ch. 7 in Monographs on Topics of Modern Mathematics Relevant to the Elementary Field (Ed. J. W. A. Young). New York: Dover, pp. 306-349, 1955.

Referenced on Wolfram|Alpha: Number Theory


Weisstein, Eric W. «Number Theory.» From MathWorld–A Wolfram Web Resource.

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